An explanation for an apparent failure of the box‐hill procedure for model discrimination

Froment and Mezaki made an early attempt to verify, by using real experimental results, that the Box-Hill procedure could accomplish more efficient model discrimination than less sophisticated procedures. They found rapid convergence but the conclusion varied, depending on the conditions of the initial experimental trials. In attempting to remedy this inconsistency several workers have found changes in the Box-Hill method which can eliminate it. In this investigation an explanation of the failure is sought and found in terms of the requirements of the method. It is shown that direct application of the unmodified procedure is successful if the dependent variable is chosen so as to minimize the effect of errors in the independent variables even though this means changing the form of the model from linear to nonlinear in the parameters. Froment et Mezaki ont les premiers essaye de verifier, an moyen de resultats experimentaux concrets, si le procede de Box et Hill pourrait permettre de realiser une discrimination plus efficace des modeles que d'autres methodes moins complexes; ils ont constate une convergence rapide, mais la conclusion variait selon les conditions des experiences initiales. En essayant de remedier a cette anomalie, plusieurs chercheurs ont trouve des modifications a la methode de Box et Hill qui permettaient d'eliminer ladite anomalie. Dans la presente etude, on a recherche une explication de l'echec en question en fonction des exigences de la methode. On indique que l'application directe de la methode non modifiee reussit, si l'on choisit la variable dependante de maniere a minimiser l'effet des erreurs dans la variable independante, bien que cela signifie qu'il faille changer dans les parametres la forme du modele de lineaire a non lineaire.